Bodyfat Comparisons
plot(BodyFat$WEIGHT, BodyFat$BODYFAT, main="BodyFat % by Weight",
xlab="Weight", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$WEIGHT), col="red")
summary(model1 <- lm(BodyFat$BODYFAT~BodyFat$WEIGHT))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$WEIGHT)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.3283 -4.2438 -0.0054 4.4562 19.8010
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.06248 2.41993 -3.745 0.000224 ***
## BodyFat$WEIGHT 0.15690 0.01332 11.781 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.107 on 248 degrees of freedom
## Multiple R-squared: 0.3588, Adjusted R-squared: 0.3563
## F-statistic: 138.8 on 1 and 248 DF, p-value: < 2.2e-16
res1 <- resid(model1)
plot(fitted(model1), res1)
abline(0,0)
plot(BodyFat$Neck.Inch., BodyFat$BODYFAT, main="BodyFat % by Neck",
xlab="Neck Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Neck.Inch.), col="red")
summary(model2 <- lm(BodyFat$BODYFAT~BodyFat$Neck.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Neck.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.0953 -4.8309 -0.2711 5.0044 21.2513
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -37.9965 6.7130 -5.66 4.17e-08 ***
## BodyFat$Neck.Inch. 3.8128 0.4475 8.52 1.57e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.708 on 248 degrees of freedom
## Multiple R-squared: 0.2264, Adjusted R-squared: 0.2233
## F-statistic: 72.59 on 1 and 248 DF, p-value: 1.569e-15
res2 <- resid(model2)
plot(fitted(model2), res2)
abline(0,0)
plot(BodyFat$Chest.Inch., BodyFat$BODYFAT, main="BodyFat % by Chest",
xlab="Chest Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Chest.Inch.), col="red")
summary(model3 <- lm(BodyFat$BODYFAT~BodyFat$Chest.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Chest.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.9505 -3.8506 -0.3307 3.4779 14.0724
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -44.8911 4.2353 -10.60 <2e-16 ***
## BodyFat$Chest.Inch. 1.6096 0.1062 15.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.495 on 248 degrees of freedom
## Multiple R-squared: 0.4808, Adjusted R-squared: 0.4787
## F-statistic: 229.7 on 1 and 248 DF, p-value: < 2.2e-16
res3 <- resid(model3)
plot(fitted(model3), res3)
abline(0,0)
plot(BodyFat$Abdomen.Inch., BodyFat$BODYFAT, main="BodyFat % by Abdomen",
xlab="Abdomen Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Abdomen.Inch.), col="red")
summary(model4 <- lm(BodyFat$BODYFAT~BodyFat$Abdomen.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Abdomen.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.194 -3.514 -0.054 3.003 11.937
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -34.34373 2.49383 -13.77 <2e-16 ***
## BodyFat$Abdomen.Inch. 1.46359 0.06787 21.56 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.498 on 248 degrees of freedom
## Multiple R-squared: 0.6522, Adjusted R-squared: 0.6508
## F-statistic: 465 on 1 and 248 DF, p-value: < 2.2e-16
res4 <- resid(model4)
plot(fitted(model4), res4)
abline(0,0)
plot(BodyFat$Hip.Inch., BodyFat$BODYFAT, main="BodyFat % by Hip",
xlab="Hip Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Hip.Inch.), col="red")
summary(model5 <- lm(BodyFat$BODYFAT~BodyFat$Hip.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Hip.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.6607 -3.6312 -0.1486 4.2709 17.6009
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -46.7149 5.3914 -8.665 5.94e-16 ***
## BodyFat$Hip.Inch. 1.6711 0.1366 12.235 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.023 on 248 degrees of freedom
## Multiple R-squared: 0.3764, Adjusted R-squared: 0.3739
## F-statistic: 149.7 on 1 and 248 DF, p-value: < 2.2e-16
res5 <- resid(model5)
plot(fitted(model5), res5)
abline(0,0)
plot(BodyFat$Thigh.Inch., BodyFat$BODYFAT, main="BodyFat % by Thigh",
xlab="Thigh Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Thigh.Inch.), col="red")
summary(model6 <- lm(BodyFat$BODYFAT~BodyFat$Thigh.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Thigh.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.7060 -4.3158 -0.0381 4.2817 23.6137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -28.4688 4.6766 -6.088 4.33e-09 ***
## BodyFat$Thigh.Inch. 2.0302 0.1989 10.206 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.4 on 248 degrees of freedom
## Multiple R-squared: 0.2958, Adjusted R-squared: 0.293
## F-statistic: 104.2 on 1 and 248 DF, p-value: < 2.2e-16
res6 <- resid(model6)
plot(fitted(model6), res6)
abline(0,0)
plot(BodyFat$Wrist.Inch , BodyFat$BODYFAT, main="BodyFat % by Wrist",
xlab="Wrist Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Wrist.Inch.), col="red")
summary(model15 <- lm(BodyFat$BODYFAT~BodyFat$Wrist.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Wrist.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.8762 -5.5830 0.0975 4.9789 25.5927
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -29.976 8.998 -3.331 0.000996 ***
## BodyFat$Wrist.Inch. 6.831 1.251 5.459 1.16e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.206 on 248 degrees of freedom
## Multiple R-squared: 0.1073, Adjusted R-squared: 0.1037
## F-statistic: 29.8 on 1 and 248 DF, p-value: 1.16e-07
res15 <- resid(model15)
plot(fitted(model15), res15)
abline(0,0)
print(cor(BodyFat$BODYFAT,BodyFat$Wrist.Inch.))
## [1] 0.3275347
plot(BodyFat$Knee.Inch , BodyFat$BODYFAT, main="BodyFat % by Knee",
xlab="Knee Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Knee.Inch.), col="red")
summary(model16 <- lm(BodyFat$BODYFAT~BodyFat$Knee.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Knee.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.9317 -4.4330 -0.2264 3.8845 28.7175
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -41.338 6.826 -6.056 5.14e-09 ***
## BodyFat$Knee.Inch. 3.973 0.448 8.868 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.645 on 248 degrees of freedom
## Multiple R-squared: 0.2408, Adjusted R-squared: 0.2377
## F-statistic: 78.65 on 1 and 248 DF, p-value: < 2.2e-16
res16 <- resid(model16)
plot(fitted(model16), res16)
abline(0,0)
print(cor(BodyFat$BODYFAT,BodyFat$Knee.Inch.))
## [1] 0.4906831
plot(BodyFat$Biceps.Inch , BodyFat$BODYFAT, main="BodyFat % by Bicep",
xlab="Bicep Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Biceps.Inch.), col="red")
summary(model17 <- lm(BodyFat$BODYFAT~BodyFat$Biceps.Inch.))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Biceps.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.4682 -5.0161 0.0371 4.6889 23.1359
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -20.0785 4.6308 -4.336 2.11e-05 ***
## BodyFat$Biceps.Inch. 3.0775 0.3624 8.492 1.88e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.713 on 248 degrees of freedom
## Multiple R-squared: 0.2253, Adjusted R-squared: 0.2222
## F-statistic: 72.12 on 1 and 248 DF, p-value: 1.885e-15
res17 <- resid(model17)
plot(fitted(model17), res17)
abline(0,0)
print(cor(BodyFat$BODYFAT,BodyFat$Biceps.Inch.))
## [1] 0.4746496
Density Comparisons
plot(BodyFat$WEIGHT, BodyFat$DENSITY, main="Density by Weight",
xlab="Weight", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$WEIGHT), col="red")
summary(model7 <- lm(BodyFat$DENSITY~BodyFat$WEIGHT))
##
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$WEIGHT)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.045518 -0.011178 -0.000312 0.009787 0.060619
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.122e+00 6.027e-03 186.09 <2e-16 ***
## BodyFat$WEIGHT -3.703e-04 3.317e-05 -11.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01521 on 248 degrees of freedom
## Multiple R-squared: 0.3345, Adjusted R-squared: 0.3318
## F-statistic: 124.6 on 1 and 248 DF, p-value: < 2.2e-16
res7 <- resid(model7)
plot(fitted(model7), res7)
abline(0,0)
plot(BodyFat$Neck.Inch., BodyFat$DENSITY, main="Density by Neck",
xlab="Neck Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Neck.Inch.), col="red")
summary(model8 <- lm(BodyFat$DENSITY~BodyFat$Neck.Inch.))
##
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Neck.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.049029 -0.012422 0.000111 0.011418 0.054720
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.188848 0.016607 71.585 < 2e-16 ***
## BodyFat$Neck.Inch. -0.008928 0.001107 -8.064 3.15e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01659 on 248 degrees of freedom
## Multiple R-squared: 0.2077, Adjusted R-squared: 0.2046
## F-statistic: 65.03 on 1 and 248 DF, p-value: 3.149e-14
res8 <- resid(model8)
plot(fitted(model8), res8)
abline(0,0)
plot(BodyFat$Chest.Inch., BodyFat$DENSITY, main="Density by Chest",
xlab="Chest Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Chest.Inch.), col="red")
summary(model9 <- lm(BodyFat$DENSITY~BodyFat$Chest.Inch.))
##
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Chest.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.031922 -0.008539 0.000361 0.009136 0.062280
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2065784 0.0106513 113.28 <2e-16 ***
## BodyFat$Chest.Inch. -0.0038091 0.0002671 -14.26 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01382 on 248 degrees of freedom
## Multiple R-squared: 0.4506, Adjusted R-squared: 0.4484
## F-statistic: 203.4 on 1 and 248 DF, p-value: < 2.2e-16
res9 <- resid(model9)
plot(fitted(model9), res9)
abline(0,0)
plot(BodyFat$Abdomen.Inch., BodyFat$DENSITY, main="Density by Abdomen",
xlab="Abdomen Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Abdomen.Inch.), col="red")
summary(model10 <- lm(BodyFat$DENSITY~BodyFat$Abdomen.Inch.))
##
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Abdomen.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.028557 -0.007219 -0.000409 0.008288 0.052866
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.1833131 0.0063080 187.59 <2e-16 ***
## BodyFat$Abdomen.Inch. -0.0035099 0.0001717 -20.45 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01138 on 248 degrees of freedom
## Multiple R-squared: 0.6276, Adjusted R-squared: 0.6261
## F-statistic: 418 on 1 and 248 DF, p-value: < 2.2e-16
res10 <- resid(model10)
plot(fitted(model10), res10)
abline(0,0)
plot(BodyFat$Hip.Inch., BodyFat$DENSITY, main="Density by Hip",
xlab="Hip Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Hip.Inch.), col="red")
summary(model11 <- lm(BodyFat$DENSITY~BodyFat$Hip.Inch.))
##
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Hip.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.040209 -0.010954 0.000160 0.008383 0.055613
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2113887 0.0134047 90.37 <2e-16 ***
## BodyFat$Hip.Inch. -0.0039672 0.0003396 -11.68 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01497 on 248 degrees of freedom
## Multiple R-squared: 0.3549, Adjusted R-squared: 0.3523
## F-statistic: 136.5 on 1 and 248 DF, p-value: < 2.2e-16
res11 <- resid(model11)
plot(fitted(model11), res11)
abline(0,0)
plot(BodyFat$Thigh.Inch., BodyFat$DENSITY, main="Density by Thigh",
xlab="Thigh Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Thigh.Inch.), col="red")
summary(model12 <- lm(BodyFat$DENSITY~BodyFat$Thigh.Inch.))
##
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Thigh.Inch.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.054421 -0.010793 -0.000279 0.010415 0.048144
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.169294 0.011520 101.504 <2e-16 ***
## BodyFat$Thigh.Inch. -0.004872 0.000490 -9.942 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01576 on 248 degrees of freedom
## Multiple R-squared: 0.285, Adjusted R-squared: 0.2821
## F-statistic: 98.85 on 1 and 248 DF, p-value: < 2.2e-16
res12 <- resid(model12)
plot(fitted(model12), res12)
abline(0,0)
Height and Weight Combo
summary(model13 <- lm(BodyFat$BODYFAT~BodyFat$WEIGHT + BodyFat$HEIGHT))
##
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$WEIGHT + BodyFat$HEIGHT)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.6967 -3.3238 -0.0994 4.1984 12.2339
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 71.10432 9.58382 7.419 1.89e-12 ***
## BodyFat$WEIGHT 0.21147 0.01333 15.866 < 2e-16 ***
## BodyFat$HEIGHT -1.27895 0.14908 -8.579 1.07e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.371 on 247 degrees of freedom
## Multiple R-squared: 0.506, Adjusted R-squared: 0.502
## F-statistic: 126.5 on 2 and 247 DF, p-value: < 2.2e-16
res13 <- resid(model13)
plot(fitted(model13), res13)
abline(0,0)
summary(model14 <- lm(BodyFat$DENSITY~BodyFat$WEIGHT + BodyFat$HEIGHT))
##
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$WEIGHT + BodyFat$HEIGHT)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.030154 -0.010359 -0.000209 0.007843 0.051994
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.214e-01 2.385e-02 38.63 < 2e-16 ***
## BodyFat$WEIGHT -5.066e-04 3.317e-05 -15.27 < 2e-16 ***
## BodyFat$HEIGHT 3.194e-03 3.710e-04 8.61 8.73e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01337 on 247 degrees of freedom
## Multiple R-squared: 0.4881, Adjusted R-squared: 0.484
## F-statistic: 117.8 on 2 and 247 DF, p-value: < 2.2e-16
res14 <- resid(model14)
plot(fitted(model14), res14)
abline(0,0)
All correlations
par(mfrow=c(4,3))
##scatter plot
print("Density Correlation:")
## [1] "Density Correlation:"
plot(BodyFat$DENSITY,BodyFat$BODYFAT)
cor(BodyFat$DENSITY,BodyFat$BODYFAT)
## [1] -0.9877761
print("Weight Correlation:")
## [1] "Weight Correlation:"
plot(BodyFat$WEIGHT,BodyFat$BODYFAT)
cor(BodyFat$WEIGHT,BodyFat$BODYFAT)
## [1] 0.5990389
print("Neck Correlation:")
## [1] "Neck Correlation:"
plot(BodyFat$Neck.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Neck.Inch.,BodyFat$BODYFAT)
## [1] 0.4758356
print("Chest Correlation:")
## [1] "Chest Correlation:"
plot(BodyFat$Chest.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Chest.Inch.,BodyFat$BODYFAT)
## [1] 0.6934283
print("DAbdomen Correlation:")
## [1] "DAbdomen Correlation:"
plot(BodyFat$Abdomen.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Abdomen.Inch.,BodyFat$BODYFAT)
## [1] 0.8075761
print("Hip Correlation:")
## [1] "Hip Correlation:"
plot(BodyFat$Hip.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Hip.Inch.,BodyFat$BODYFAT)
## [1] 0.6135076
print("Thigh Correlation:")
## [1] "Thigh Correlation:"
plot(BodyFat$Thigh.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Thigh.Inch.,BodyFat$BODYFAT)
## [1] 0.5438656
print("Knee Correlation:")
## [1] "Knee Correlation:"
plot(BodyFat$Knee.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Knee.Inch.,BodyFat$BODYFAT)
## [1] 0.4906831
print("Ankle Correlation:")
## [1] "Ankle Correlation:"
plot(BodyFat$Ankle.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Ankle.Inch.,BodyFat$BODYFAT)
## [1] 0.2514156
print("Bicep Correlation:")
## [1] "Bicep Correlation:"
plot(BodyFat$Biceps.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Biceps.Inch.,BodyFat$BODYFAT)
## [1] 0.4746496
